Weight and Gravity vs Field Forces

Weight is the gravitational force that a planet or other body exerts on an object, W = mg, measured in newtons, while mass is the amount of matter in the object, measured in kilograms and the same everywhere; gravity is one of the field forces, along with electric and magnetic forces, that act without contact. In brief: the gravitational field strength g is the force per unit mass (N/kg), equal to 9.8 N/kg at Earth’s surface, 1.6 N/kg on the Moon and 3.7 N/kg on Mars. A person’s mass does not change on the Moon, but the weight is about one-sixth.

People often say “weight” when they mean “mass”. In physics the two are different quantities with different units. This guide defines weight, gravity and gravitational field strength, explains field forces in general, compares mass and weight in a table, works through calculations for different planets and corrects common mistakes.

What is weight?

Weight is the force of gravity acting on an object. Its formula is W = mg, where m is mass and g is the gravitational field strength at that place. Weight is a vector, pointing toward the center of the planet (downward). It is measured with a spring balance in newtons. Weight changes with location: g is slightly smaller at the equator and on mountains than at the poles and at sea level, and much smaller on the Moon.

The “weight” read by a bathroom scale is really the normal force on the person’s feet, and it is calibrated to display kilograms. In an accelerating elevator, the apparent weight changes, though mass does not. In orbit, astronauts are in free fall, so they feel “weightless”, though the gravity on them is still about 90 percent of that on the ground at the height of the International Space Station.

What is gravity?

Gravity is the attractive force between any two masses. According to Newton’s law of universal gravitation, F = Gm₁m₂ ÷ r², with G = 6.67 × 10⁻¹¹ N·m²/kg². For everyday objects the force is extremely small, and only noticeable when one of the masses is as large as a planet. The gravitational field strength g = F ÷ m is the force per unit mass on a small test mass. At the surface of a planet of mass M and radius R, g = GM ÷ R².

What are field forces?

A field is a region where an object experiences a force without touching the source. The gravitational field acts on masses, the electric field on charges, and the magnetic field on magnets and moving charges. Field forces are non-contact forces. In a uniform field, such as the gravitational field near the ground, the force on an object is the same everywhere. Field lines are drawn to show the direction of the force and, by their spacing, its strength.

Mass and weight compared

Worked example: weight on different bodies

An astronaut with a mass of 70 kg and equipment of 30 kg. Use g = 9.8 N/kg on Earth, 1.6 N/kg on the Moon, 3.7 N/kg on Mars.

1. Total mass: 70 + 30 = 100 kg, the same on all three bodies.
2. Weight on Earth: 100 × 9.8 = 980 N.
3. Weight on the Moon: 100 × 1.6 = 160 N. The ratio to Earth is 160 ÷ 980 = 0.16, about one-sixth.
4. Weight on Mars: 100 × 3.7 = 370 N.
5. Field strength from a measurement: if a 2.0 kg object weighs 7.4 N on an unknown planet, g = W ÷ m = 7.4 ÷ 2.0 = 3.7 N/kg, which corresponds to Mars.

How was gravity understood?

Aristotle thought that heavy objects fall faster, and Galileo showed that they accelerate equally. Newton published the law of universal gravitation in 1687, and Henry Cavendish measured G in 1798 with a torsion balance, which allowed the mass of the Earth to be calculated. Einstein’s general theory of relativity (1915) describes gravity as the curvature of spacetime, and gravitational waves were first detected directly in 2015.

Which mistakes are common?

Mistake 1: Giving weight in kilograms

Weight is a force, so it is in newtons. The kilogram is a unit of mass.

Mistake 2: Saying that astronauts in orbit have no gravity

Gravity is still strong there. They feel weightless because they are in free fall.

Mistake 3: Thinking that mass changes on the Moon

Mass stays the same. The weight decreases.

Mistake 4: Confusing g (field strength) with G (constant)

g depends on the planet and location, and G is a universal constant.